Aperiodic Semigroup

Semigroup S such that every element x ∈ S is aperiodic
defining formula
\forall x \exists n, x^n = x^{n+1}
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In mathematics, an aperiodic semigroup is a semigroup S such that every element x ∈ S is aperiodic, that is, for each x there exists a positive integer n such that xn = xn + 1. An aperiodic monoid is an aperiodic semigroup which is a monoid.
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Aperiodic monoid
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